How can i make a low poly flame animation in Blender
I took a quick stab at this with a Sculpted mesh using Dynotopo symmetry off with a pixel setting of 12.

The rest was done with just animating an empty, and using that empty as the referenced object in a displacement modifier with a magic texture.

This was about 10 minutes worth of work if you happen to be efficient in Blender.

Hence I'm sure you could spend a little more time if you want it to look as good as it does in your reference.

I would imagine that an animated loop of upward flying diamond shapes at the same speed and the same material would sell the flying ember effect.

Here's the fruit of my 10 minutes (the difference between the two are texture selection &amp; empty animation differences only):

Attempt #1:


Attempt #2:




Per request here is the Blend File:
I've also included an action within it for you associated to a "Fake" user.
As of Right now, the animation wont start until you hit frame 15.
In the NLA editor just drag the action back to the beginning frame (highlight it and hit G >> Drag to the left) to watch the full animation from the start.

As for a sprite sheet, I really recommend watching the video I linked to in the comments. 

Here is a Sprite sheet that I rendered out from this file: